Question

The number of toy kangaroos, K, in a toy box after 't' days is given by `K=t^2+20t`. Estimate the rate at which the number of kangaroos is changing after 3 days?

`K=t^2+20t`

Answer 1

After 3 days, the number of kangaroos is increasing by 26 kangaroos per day.

Explanation:

The rate of change of a function is the derivative of that function.

First take the derivative of `K=t^2+20t`.
The derivative of `t^n` is `nt^(n-1)` by the power rule.
So the derivative of `t^2` is `2t`.
The derivative of `at` is just `a`, so the derivative of `20t` is just `20`.
You should end up with `K'=2t+20` when you add them together.

The question wants to know the rate of change after 3 days, so just plug in 3:
`K'=2(3)+20`
`K'=26`
So there you have it- after 3 days, the number of kangaroos is increasing by 26 kangaroos per day.